On Isometric Immersion of Three-Dimensional Geometries SL_2, Nil and Sol into a Four-Dimensional Space of Constant Curvature - Masal'tsev, L. A. (Ukrains’kyi Matematychnyi Zhurnal, 2005)
We prove the nonexistence of isometric immersion of geometries Nil^3, SL_2 into the four-dimensional space M_c^4 of the constant curvature c. We establish that the geometry Sol^3 cannot be immersed into M_c^4 if c eq -1 and find the analytic immersion of this geometry into the hyperbolic space H^4(-1).